Theorem confun3

Description: Confun's more complex form where both a,d have been "defined". (Contributed by Jarvin Udandy, 6-Sep-2020)

	Ref	Expression
Hypotheses	confun3.1	|- ( ph <-> ( ch -> ps ) )
	confun3.2	|- ( th <-> -. ( ch -> ( ch /\ -. ch ) ) )
	confun3.3	|- ( ch -> ps )
	confun3.4	|- ( ch -> -. ( ch -> ( ch /\ -. ch ) ) )
	confun3.5	|- ( ( ch -> ps ) -> ( ( ch -> ps ) -> ps ) )
Assertion	confun3	|- ( ch -> ( -. ( ch -> ( ch /\ -. ch ) ) <-> ( ch -> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		confun3.1	|- ( ph <-> ( ch -> ps ) )
2		confun3.2	|- ( th <-> -. ( ch -> ( ch /\ -. ch ) ) )
3		confun3.3	|- ( ch -> ps )
4		confun3.4	|- ( ch -> -. ( ch -> ( ch /\ -. ch ) ) )
5		confun3.5	|- ( ( ch -> ps ) -> ( ( ch -> ps ) -> ps ) )
6	3 3 4 5	confun	|- ( ch -> ( -. ( ch -> ( ch /\ -. ch ) ) <-> ( ch -> ps ) ) )